Skip to main content
SpringerLink
Log in
Book cover

Advances in Structural Optimization pp 1–45Cite as

Finite Element Based Engineering Design Sensitivity Analysis and Optimization

  • Chapter

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 25))

Abstract

The aim of this paper is to present basic concepts and selected finite element based methods and tools for sensitivity analysis and rational engineering design and optimization of mechanical structures and components. The main emphasis is devoted to sensitivity and optimization problems that involve shape and sizing design variables.

The methods are selected from conditions of versatility, computational efficiency, and suitability for integration into an engineering design optimization system which realizes the design process as an iterative solution procedure of a multicriterion optimization problem based on the concept of integration of finite element analysis, sensitivity analysis, and optimization by mathematical programming. Typical design objectives that may enter into the multicriterion problem formulation include, e.g., structural cost, displacements and stresses from static and thermal loads, and structural vibration frequencies and buckling loads.

For these types of objectives, expressions for design sensitivities are derived, and the paper presents a new approach to semi-analytical design sensitivity analysis which is easy to implement as an integral part of the finite element analysis. The new approach is computationally inexpensive, and completely eliminates severe sensitivity errors that may occur in problems of semi-analytical shape design sensitivity analysis and optimization of certain types of structures. Such errors have been reported in several papers in recent years.

Use of the methods presented in this paper is illustrated by examples.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Arora, J.S. (1989): Interactive Design Optimization of Structural Elements. In: Discretization Methods and Structural Optimization -Procedures and Applications, (Eds. H.A. Eschenauer & G. Thierauf), pp. 10–16, Springer-Verlag, Berlin.

    Google Scholar 

  • Atrek, E. R.; Gallagher, R.H.; Ragsdell, K.M.; Zienkiewicz, O.C. (1984) (Eds.): New Directions in Optimum Structural design, John Wiley & Sons, New York.

    MATH  Google Scholar 

  • Barthelemy, B.; Haftka, R.T. (1988): Accuracy Analysis of the Semi-Analytical Method for Shape Sensitivity Analysis. AIAA Paper 88–2284, Proc. AIAA/ASME/ASCE/ASC 29th Structures, Structural Dynamics and Materials Conference, Part 1, pp. 562–581.

    Google Scholar 

  • Barthelemy, B.; Haftka, R.T. Mechanics of Structures and Machines., Vol. 18, pp. 407–432 (1990).

    Google Scholar 

  • Bendsøe, M.P.; Mota Soares, C.A. (1993) (Eds.): Topology Design of Structures, Kluwer, Dordrecht, The Netherlands.

    Google Scholar 

  • Bendsøe, M.P. (1994): Methods for the Optimization of Structural Topology, Shape and Material. Mathematical Institute, Technical University of Denmark, Lyngby, Denmark, 299 pp.

    Google Scholar 

  • Bendsøe, M.P. (1989): Optimal Shape as a Material Distribution Problem. Structural Optimization, Vol. 1, No. 4, pp. 193–202.

    Google Scholar 

  • Bendsøe, M.P.; Kikuchi, N. (1988): Generating Optimal Topologies in Structural Design Using a Homogenization Method. Computer Methods in Applied Mechanics and Engineering, Vol. 117, pp. 197–224.

    Google Scholar 

  • Bendsøe, M.P.; Olhoff, N.; Taylor, J.E. (1983): A Variational Formulation for Multicriteria Structural Optimization. J. Struct. Mech., Vol. 11, pp. 523–544.

    Google Scholar 

  • Bennett, J.A.; Botkin, M.E. (1985): Structural Shape Optimization with Geometric Description and Adaptive Mesh Refinement. AIAA Journal, Vol. 23, No. 3, pp. 458–464.

    ADS  Google Scholar 

  • Bennett, J.A.; Botkin, M.E. (1986) (Eds.): The Optimum Shape. Automated Structural Design, Plenum Press, New York.

    Google Scholar 

  • Botkin, M.E.; Yang, R.J.; Bennett, J.A. (1986): Shape Optimization of Three-dimensional Stamped and Solid Automotive Components. In: The Optimum Shape. Automated Structural Design (Eds. J.A. Bennett & M.E. Botkin), pp. 235–262, Plenum Press, New York.

    Google Scholar 

  • Braibant, V.; Fleury, C. (1984): Shape Optimal Design Using B-splines. Computer Methods in Applied Mechanics and Engineering, Vol. 44, pp. 247–267.

    ADS  MATH  Google Scholar 

  • Bratus, A.S.; Seyranian, A.P. (1983): Bimodal Solutions in Eigenvalue Optimization Problems. Prikl. Matem. Mekhan., Vol. 47, No. 4, pp. 546–554

    MathSciNet  Google Scholar 

  • Applied Mathematics in Mechanics, Vol. 47, pp. 451–457.

    MathSciNet  ADS  Google Scholar 

  • Cea, J. (1981): Problems of Shape Optimal Design. In: Optimization of Distributed Parameter Structures (Eds. E.J. Haug & J. Cea), Vol. 2, pp. 1005–1048, Sijthoff & Nordhoff, The Netherlands.

    Google Scholar 

  • Cheng, G.; Gu, Y.; Zhou, Y. (1989): Accuracy of Semi-Analytical Sensitivity Analysis. Finite Elements in Analysis and Design, Vol. 6, pp. 113–128.

    MATH  Google Scholar 

  • Cheng, G.; Liu, Y. (1987): A New Computational Scheme for Sensitivity Analysis. Engineering Optimization, Vol. 12, pp. 219–235.

    Google Scholar 

  • Cheng, G.; Olhoff, N. (1991): New Method of Error Analysis and Detection in Semi-analytical Sensitivity Analysis. Report No. 36, Institute of Mechanical Engineering, Aalborg University, Denmark, 34 pp.

    Google Scholar 

  • Cheng, G.; Olhoff, N. (1993): Rigid Body Motion Test Against Error in Semi-Analytical Sensitivity Analysis. Computers & Structures, Vol. 46, No. 3, pp. 515–527.

    ADS  MATH  Google Scholar 

  • Choi, K.K.; Chang, K.-H. (1991): Shape Design Sensitivity Analysis and What-If Workstation For Elastic Solids. Technical Report R-105, Center for Simulation and Design Optimization and Department of Mechanical Engineering, The University of Iowa, 33 pp.

    Google Scholar 

  • Choi, K.K. (1985): Shape Design Sensitivity Analysis of Displacements and Stress Constraints. Journal of Structural Mechanics, Vol. 13, pp. 27–41.

    MathSciNet  Google Scholar 

  • Choi, K.K.; Twu, S.-L. (1988): On Equivalence of Continuum and Discrete Methods of Shape Sensitivity Analysis. AIAA Journal, Vol. 27, No. 10, pp. 1418–1424.

    MathSciNet  ADS  Google Scholar 

  • Courant, R.; Hilbert, D. (1953): Methods of Mathematical Physics, Vol. 1, Interscience Publishers, New York.

    Google Scholar 

  • Dems, K.; Mróz, Z. (1983): Variational Approach by Means of Adjoint Systems to Structural Optimization and Sensitivity Analysis -1 Variation of Material Parameters within Fixed Domain. International Journal of Solids and Structures, Vol. 19, pp. 677–692.

    MathSciNet  MATH  Google Scholar 

  • Dems, K.; Mróz, Z. (1984): Variational Approach by Means of Adjoint Systems to Structural Optimization and Sensitivity Analysis -II Structure Shape Variation. International Journal of Solids and Structures, Vol. 20, pp. 527–552.

    MathSciNet  MATH  Google Scholar 

  • Dems, K.; Mróz, Z. (1993): On Shape Sensitivity Approaches in the Numerical Analysis of Structures. Structural Optimization, Vol. 6, pp. 86–93.

    Google Scholar 

  • Dhatt, G.; Touzot, G. (1984): The Finite Element Method Displayed, Wiley & Sons, New York.

    MATH  Google Scholar 

  • Ding, Y. (1986): Shape Optimization of Structures: a Literature Survey. Computers and Structures, Vol. 24, No. 6, pp. 985–1004.

    MathSciNet  MATH  Google Scholar 

  • Eschenauer, H.A.; Olhoff, N. (1983) (Eds.): Optimization Methods in Structural Design, B.I.-Wissenschaftsverlag, Mannheim.

    MATH  Google Scholar 

  • Eschenauer, H.A. (1986): Numerical and Experimental Investigations of Structural Optimization of Engineering Designs. Siegen: Bonn+Fries, Druckerei und Verlag.

    Google Scholar 

  • Eschenauer, H.A.; Mattheck, C.; Olhoff, N. (1991) (Eds.): Engineering Optimization in Design Processes, Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • Eschenauer, H.A.; Thierauf, G. (1989) (Eds.): Discretization Methods and Structural Optimization -Procedures and Applications, Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • Esping, B.J.D. (1983): Minimum Weight Design of Membrane Structures, Ph.D. Thesis, Dept. Aeronautical Structures and Materials, The Royal Institute of Technology, Stockholm, Report 83–1.

    Google Scholar 

  • Esping, B.J.D. (1984): Minimum Weight Design of Membrane Structures Using Eight Node Isoparametric Elements and Numerical Derivatives. Computers and Structures, Vol. 19, No. 4, pp. 591–604.

    Google Scholar 

  • Esping, B.J.D. (1986): The OASIS Structural Optimization System. Computers & Structures, Vol. 23, No. 3, pp. 365–377.

    MathSciNet  Google Scholar 

  • Fenves, P.A.; Lust, R.V. (1991): Error Analysis of Semi-Analytical Displacement Derivatives for Shape and Sizing Variables. AIAA Journal, Vol. 29, pp. 271–279.

    ADS  Google Scholar 

  • Fleury, C. (1989): CONLIN: An Efficient Dual Optimizer Based On Convex Approximation Concepts. Structural Optimization, Vol. 1, pp. 81–89.

    Google Scholar 

  • Fleury, C.; Braibant, V. (1986): Structural Optimization: A New Dual Method Using Mixed Variables. International Journal for Numerical Methods in Engineering, Vol. 23, 409–428.

    MathSciNet  ADS  MATH  Google Scholar 

  • Gajewski, A.; Zyczkowski, M. (1988): Optimal Structural Design Under Stability Constraints, Kluwer Academic Publishers, Dordrecht-Boston-London.

    MATH  Google Scholar 

  • Gilmore, B.J.; Hoeltzel, D.A.; Azarm, S.; Eschenauer, H.A. (1993) (Eds.): Advances in Design Automation. Proc. 1993 ASME Design Technical Conferences -19th Design Automation Conference, Albuquerque, New Mexico, The American Society of Mechanical Engineers, New York.

    Google Scholar 

  • Haber, R.B. (1987): A New Variational Approach to Structural Shape Sensitivity Analysis. In: Computer Aided Optimal Design: Structural and Mechanical Systems (Ed. C.A. Mota Soares), pp. 573–587, Springer-Verlag, Berlin.

    Google Scholar 

  • Haftka, R.T.; Adelman, H.M. (1989): Recent Developments in Structural Sensitivity Analysis. Structural Optimization, Vol. 1, pp. 137– 151.

    Google Scholar 

  • Haftka, R.T.; Grandhi, R.V. (1986): Structural Shape Optimization -A Survey. Computer Methods in Applied Mechanics and Engineering, Vol. 57, pp. 91–106.

    MathSciNet  ADS  MATH  Google Scholar 

  • Haug, E.J. (1993) (Ed.): Concurrent Engineering: Tools and Technologies for Mechanical System Design, 998 pp., Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • Haug, E.J.; Cea, J. (1981) (Eds.): Optimization of Distributed Parameter Structures, Vol. 1: pp. 1–842, Vol. 2: pp. 843–1609, Sijthoff & Nordhoff, The Netherlands.

    Google Scholar 

  • Haug, E.J. (1981): A Review of Distributed Parameter Structural Optimization Literature. In: Optimization of Distributed Parameter Structures (Eds. E.J. Haug & J. Cea), Vol. 1, pp. 3–74, Sijthoff & Nordhoff, The Netherlands.

    Google Scholar 

  • Haug, E.J.; Choi, K.K.; Komkov, V. (1986): Design Sensitivity Analysis of Structural Systems, Academic Press, New York.

    MATH  Google Scholar 

  • Haug, E.J.; Rousselet, B. (1980b): Design Sensitivity Analysis in Structural Mechanics. II: Eigenvalue Variations. Journal of Structural Mechanics, Vol. 8, No. 2, pp. 161–186.

    MathSciNet  Google Scholar 

  • Herskovits, J. (1993) (Ed.): Proc. Structural Optimization ’93 -The World Congress on Optimal Design of Structural Systems, Vol. 1 & 2. Federal University of Rio de Janeiro, Brazil.

    Google Scholar 

  • Hörnlein, H.R.E.M. (1987): Take-off in Optimum Structural Design. In: Computer Aided Optimal Design. Structural and Mechanical Systems (Ed. C.A. Mota Soares), NATO ASI Series F: Computer and System Sciences, Vol. 27, pp. 901–919, Springer-Verlag, Berlin.

    Google Scholar 

  • Kristensen, E.S.; Madsen, N.F. (1976): On the Optimum Shape of Fillets in Plates Subjected to Multiple In-plane Loading Cases. International Journal for Numerical Methods in Engineering, Vol. 10, pp. 1007–1019.

    ADS  MATH  Google Scholar 

  • Lancaster, P. (1964): On Eigenvalues of Matrices Dependent on a Parameter. Numerische Mathematik, Vol. 6, pp. 377–387.

    MathSciNet  MATH  Google Scholar 

  • Lund, E. (1993): Design Sensitivity Analysis of Finite Element Discretized Structures. Report No. 55, Institute of Mechanical Engineering, Aalborg University, Denmark, 31 pp. Earlier version published in: Lecture Notes for COMETT course on Computer Aided Optimum Design of Structures, August 1993, Aalborg.

    Google Scholar 

  • Lund, E.; Olhoff, N. (1993a): Reliable and Efficient Finite Element Based Design Sensitivity Analysis of Eigenvalues. In: Proc. Structural Optimization 93 -The World Congress on Optimal Design of Structural Systems. (Ed. J. Herskovits), Vol. 2, pp. 197–204, Rio de Janeiro, Brazil.

    Google Scholar 

  • Lund, E.; Olhoff, N. (1993b): Shape Design Sensitivity Analysis of Eigenvalues Using “Exact” Numerical Differentiation of Finite Element Matrices. Report No. 54, Institute of Mechanical Engineering, Aalborg University, Denmark, 19 pp. Structural Optimization (submitted).

    Google Scholar 

  • Lund, E.; Rasmussen, J. (1994): A General and Flexible Method of Problem Definition in Structural Optimization Systems. Report No. 58, Institute of Mechanical Engineering, Aalborg University, Denmark, 18 pp. Structural Optimization (submitted).

    Google Scholar 

  • Masur, E.F. (1984): Optimal Structural Design under Multiple Eigenvalue Constraints. International Journal of Solids and Structures, Vol. 20, pp. 211–231.

    MathSciNet  MATH  Google Scholar 

  • Masur, E.F. (1985): Some Additional Comments on Optimal Structural Design under Multiple Eigenvalue Constraints. International Journal of Solids and Structures, Vol. 21, pp. 117–120.

    MathSciNet  MATH  Google Scholar 

  • Mlejnek, H.P. (1992): Accuracy of Semi-analytical Sensitivities and Its Improvement by the “Natural Method”. Structural Optimization, Vol. 4, pp. 128–131.

    ADS  Google Scholar 

  • Morris, A.J. (1982) (Ed.): Foundations of Structural Optimization: A Unified Approach, Chichester, England.

    Google Scholar 

  • Mota Soares, C.A. (1987) (Ed.): Computer Aided Optimal Design: Structural and Mechanical Systems, Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • Olhoff, N. (1989): Multicriterion Structural Optimization Via Bound Formulation and Mathematical Programming. Structural Optimization, Vol. 1, pp. 11–17.

    Google Scholar 

  • Olhoff N.; Bendsøe, M.P.; Rasmussen, J. (1991): On CAD-integrated Structural Topology and Design Optimization. Computer Methods in Applied Mechanics and Engineering, Vol. 89, pp. 259–279.

    ADS  Google Scholar 

  • Olhoff, N.; Lund, E.; Rasmussen, J. (1993): Concurrent Engineering Design Optimization In a CAD Environment. In: Concurrent Engineering: Tools and Technologies for Mechanical System Design (Ed. E.J. Haug), pp. 523–586, Springer-Verlag, Berlin (1993).

    Google Scholar 

  • Olhoff, N.; Rasmussen, J. (1991a): Study of Inaccuracy in Semi-Analytical Sensitivity Analysis -A Model Problem. Structural Optimization, Vol. 3, pp. 203–213.

    Google Scholar 

  • Olhoff, N.; Rasmussen, J. (1991b): Method of Error Elimination for a Class of Semi-Analytical Sensitivity Analysis Problems. In: Engineering Optimization in Design Processes (Eds. H.A. Eschenauer, C. Mattheck & N. Olhoff), pp. 193–200, Springer-Verlag, Berlin.

    Google Scholar 

  • Olhoff N.; Rasmussen, J.; Lund, E. (1993): A Method of “Exact” Numerical Differentiation for Error Elimination in Finite Element Based Semi-Analytical Shape Sensitivity Analysis. Mechanics of Structures and Machines, Vol. 21, pp. 1–66.

    MathSciNet  Google Scholar 

  • Olhoff, N.; Krog, L.; Thomsen, J. (1993): Bi-material Topology Optimization. In: Proc. Structural Optimization ’93 -The World Congress on Optimal Design of Structural Systems (Ed. J. Herskovits), Federal University of Rio de Janeiro, Brazil, Vol.1, pp. 327–334.

    Google Scholar 

  • Olhoff, N.; Rasmussen, S.H. (1977): On Single and Bimodal Optimum Buckling Loads of Clamped Columns. International Journal of Solids and Structures, Vol. 13, pp. 605–614.

    MATH  Google Scholar 

  • Olhoff, N.; Taylor, J.E. (1983): On Structural Optimization. Journal of Applied Mechanics, Vol. 50, pp. 1139–1151.

    MathSciNet  ADS  MATH  Google Scholar 

  • Pedersen, P. (1993a) (Ed.): Optimal Design with Advanced Materials, Elsevier, The Netherlands.

    Google Scholar 

  • Pedersen, P. (1993b): Concurrent Engineering Design with and of Advanced Materials. In: Concurrent Engineering: Tools and Technologies for Mechanical System Design (Ed. E.J. Haug), pp. 627–670, Springer-Verlag, Berlin.

    Google Scholar 

  • Pedersen, P. (1991): On Thickness and Orientational Design with Orthotropic Materials. Structural Optimization, Vol. 3, pp. 69–78.

    Google Scholar 

  • Pedersen, P. (1990): Bounds on Elastic Energy in Solids of Orthotropic Materials. Structural Optimization, Vol. 2, pp. 55–63.

    Google Scholar 

  • Pedersen, P. (1989): On Optimal Orientation of Orthotropic Materials. Structural Optimization, Vol. 1, pp. 101–106.

    Google Scholar 

  • Pedersen, P.; Cheng, G.; Rasmussen, J. (1989): On Accuracy Problems for Semi-Analytical Sensitivity Analysis. Mechanics of Structures and Machines, Vol. 17, No. 3, pp. 373–384.

    Google Scholar 

  • Pedersen, P. (1983): A Unified Approach to Optimal Design. In: Optimization Methods in Structural Design (Eds. H.A. Eschenauer & N. Olhoff), pp. 182–187, B.I.-Wissenschaftsverlag, Mannheim.

    Google Scholar 

  • Pedersen, P.; Laursen, C.L. (1983): Design for Minimum Stress Concentration by Finite Elements and Linear Programming. Journal of Structural Mechanics, Vol. 10, No. 4, pp. 375–391.

    Google Scholar 

  • Pedersen, P. (1981): Design with Several Eigenvalue Constraints by Finite Elements and Linear Programming. Journal of Structural Mechanics, Vol. 10, No. 3, pp. 243–271.

    Google Scholar 

  • Rasmussen, J. (1989): Development of the Interactive Structural Shape Optimization System CAOS (in Danish), Ph.D. thesis, Institute of Mechanical Engineering, Aalborg University, Denmark, Special Report No. la.

    Google Scholar 

  • Rasmussen, J. (1990): The Structural Optimization System CAOS. Structural Optimization, Vol. 2, pp. 109–115.

    Google Scholar 

  • Rasmussen, J. (1991): Shape Optimization and CAD. International Journal of Systems Automation: Research and Applications (SARA), Vol. 89, pp. 259–279.

    Google Scholar 

  • Rasmussen, J.; Lund, E.; Birker, T. (1992): Collection of Examples, CAOS Optimization System, 3rd edition. Special Report No. lc, Institute of Mechanical Engineering, Aalborg University, Denmark, 119 pp.

    Google Scholar 

  • Rasmussen, J.; Lund, E.; Birker, T.; Olhoff, N. (1993): The CAOS System. International Series of Numerical Mathematics, Vol. 110, pp. 75–96, Birkhäuser Verlag, Basel.

    Google Scholar 

  • Rasmussen, J.; Lund, E.; Olhoff, N. (1993a): Parametric Modeling and Analysis for Optimum Design. In: Proc. Structural Optimization 93 -The World Congress on Optimal Design of Structural Systems, (Ed. J. Herskovits), Vol. 2, pp. 407–414, Rio de Janeiro, Brazil.

    Google Scholar 

  • Rasmussen, J.; Lund, E.; Olhoff, N. (1993b): Integration of Parametric Modeling and Structural Analysis for Optimum Design. In: Proc. Advances in Design Automation, The American Society of Mechanical Engineers, (Eds. Gilmore et. al.), Albuquerque, New Mexico, USA, 1993.

    Google Scholar 

  • Rasmussen, J.; Lund, E.; Olhoff, N.; Birker, T. (1993): Structural Topology and Shape Optimization with the CAOS System. In Lecture Notes for COMETT course on Computer Aided Optimal Design, February 1993, Eindhoven.

    Google Scholar 

  • Rasmussen, J.; Olhoff, N.; Lund, E. (1992): Foundations for Optimum Design System Development. In Lecture Notes for: Advanced TEMPUS course on Numerical Methods in Computer Optimal Design, 11–15 maj 1992, Zakopane, Poland.

    Google Scholar 

  • Rozvany, G.I.N.; Karihaloo, B.L. (1988) (Eds.): Structural Optimization, Kluwer, Dordrecht, The netherlands.

    Google Scholar 

  • Rozvany, G.I.N. (1993) (Ed): Optimization of Large Structural Systems, Vol. 1: pp. 1–622, Vol. 2: pp. 623–1198, Kluwer, Dordrecht, The Netherlands.

    Google Scholar 

  • Santos, J.L.T.; Choi, K.K. (1989): Integrated Computational Considerations for Large Scale Structural Design Sensitivity Analysis and Optimization. In: Discretization Methods and Structural Optimization -Procedures and Applications, (Eds. H.A. Eschenauer & G. Thierauf), pp. 299–307, Springer-Verlag, Berlin.

    Google Scholar 

  • Schmit, L.A. (1982): Structural Synthesis -Its Genesis and Development. AIAA Journal, Vol. 20, pp. 992–1000.

    Google Scholar 

  • Seyranian, A.P. (1987): Multiple Eigenvalues in Optimization Problems. Prikl. Mat. Mekh., Vol. 51, pp. 349–352; Also Applied Mathematics in Mechanics, Vol. 51, pp. 272–275.

    MathSciNet  Google Scholar 

  • Seyranian, A.P.; Lund, E.; Olhoff, N. (1994): Multiple Eigenvalues in Structural Optimization Problems. Special Report No. 21, Institute of Mechanical Engineering, Aalborg University, Denmark, 51 pp. Structural Optimization (to appear).

    Google Scholar 

  • Sobieszanski-Sobieski, J.; Rogers, J.L. (1984): A Programming System for Research and Applications in Structural Optimization. In: New directions in optimum structural design (Eds. E. Atrek, R.H. Gallagher, K.M. Ragsdell & O.C. Zienkiewicz), pp. 563–585, John Wiley & Sons, New York.

    Google Scholar 

  • Stanton, E.L. (1986): Geometric Modeling for Structural and Material Shape Optimization. In: The Optimum Shape. Automated Structural Design (Eds. J.A. Bennett & M.E. Botkin), pp. 365–383, Plenum Press, New York.

    Google Scholar 

  • Svanberg, K. (1987): The Method of Moving Asymptotes -A New Method For Structural Optimization. International Journal for Numerical Methods in Engineering, Vol. 24, pp. 359–373.

    MathSciNet  ADS  MATH  Google Scholar 

  • Taylor, J.E.; Bendsøe, M.P. (1984): An Interpretation of Min-Max Structural Design Problems Including a Method for Relaxing Constraints. International Journal of Solids and Structures, Vol. 20, pp. 301–314.

    MathSciNet  MATH  Google Scholar 

  • Yang, R.J.; Botkin, M.E. (1986): The Relationship Between the Variational Approach and the Implicit Differentiation Approach to Shape Design Sensitivities. In: The Optimum Shape. Automated Structural Design (Eds. J.A. Bennett & M.E. Botkin), pp. 61–77, Plenum Press, New York.

    Google Scholar 

  • Zienkiewicz, O.C.; Campbell, J.S. (1973): Shape Optimization and Sequential Linear Programming. In: Optimum Structural Design, Theory and Applications (Eds. R.H. Gallagher & O.C.Zienkiewicz), Wiley and Sons, London, pp. 109–126.

    Google Scholar 

  • Zolesio, J.-P. (1981): The Material Derivative (or Speed) Method for Shape Optimization. In: Optimization of Distributed Parameter Structures (Eds. E.J. Haug & J. Cea), Vol. 2, pp. 1089–1151, Sijthoff & Nordhoff, The Netherlands.

    Google Scholar 

  • Zyczkowski, M. (1989) (ed.): Structural Optimization Under Stability and Vibration Constraints. Springer, Wien -New York.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mechanical Engineering, Aalborg University, DK-9220, Aalborg, Denmark

    Niels Olhoff & Erik Lund

Authors
  1. Niels Olhoff
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Erik Lund
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Mechanical Engineering Program, COPPE/Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

    José Herskovits

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Olhoff, N., Lund, E. (1995). Finite Element Based Engineering Design Sensitivity Analysis and Optimization. In: Herskovits, J. (eds) Advances in Structural Optimization. Solid Mechanics and Its Applications, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0453-1_1

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-0453-1_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4203-1

  • Online ISBN: 978-94-011-0453-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation